There is a circular tube in a vertical plane. Two liquids which do not mix and of densities `d_1 and d_2` are filled in the tube. Each liquid subtends `90^@` angle at centre. Radius joining their interface make an angle `alpha` with vertical. Ratio `(d_1)/(d_2)` is :

Options

A. `(1+tan alpha)/(1-tan alpha)`
B. `(1+sin alpha)/(1-cos alpha)`
C. `(1+sin alpha)/(1-sin alpha)`
D. `(1+cos alpha)/(1-cos alpha)`

Answer

A

Explanation

the pressure at A due to liquid of density `d_(1)`
`=(R cos alpha - R sin alpha)d_(1) g`
Pressure at A due to liquid of density `d_(2)`
`=(R cos alpha + R sin alpha)d_(2) g`
Let, `p_(0)` = Pressure due to air in tube. Equating pressure at A, we get
`P_(0)+(R cos alpha - R sin alpha)d_(1) g`
`=P_(0) +(R cos alpha +R sin alpha)d_(2) g`
or `(d_(1))/(d_(2))=(cos alpha+sin alpha)/(cos alpha-sin alpha) =(1+tan alpha)/(1-tan alpha)`